Question: Simplify; express your answer in exponential form. Assume $k\neq 0, p\neq 0$. $\dfrac{{(kp^{-5})^{-2}}}{{(k^{-3}p)^{-4}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(kp^{-5})^{-2} = (k)^{-2}(p^{-5})^{-2}}$ On the left, we have ${k}$ to the exponent ${-2}$ . Now ${1 \times -2 = -2}$ , so ${(k)^{-2} = k^{-2}}$ Apply the ideas above to simplify the equation. $\dfrac{{(kp^{-5})^{-2}}}{{(k^{-3}p)^{-4}}} = \dfrac{{k^{-2}p^{10}}}{{k^{12}p^{-4}}}$ Break up the equation by variable and simplify. $\dfrac{{k^{-2}p^{10}}}{{k^{12}p^{-4}}} = \dfrac{{k^{-2}}}{{k^{12}}} \cdot \dfrac{{p^{10}}}{{p^{-4}}} = k^{{-2} - {12}} \cdot p^{{10} - {(-4)}} = k^{-14}p^{14}$